passover - Why is Hallel different in Sukkot and Pesach (chol ha-moed)?

During chol ha-moed (intermediate days) of Sukkot we recite a full Hallel but during chol ha-moed of Pesach (and also Rosh Chodesh and some other days) we recite a "half Hallel" (really more like 85% hallel). Sukkot and Pesach are both chagim (festivals) and so I would naively expect them to have the same liturgical status. Why the difference? I can think of a couple possibilities:

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  An unanswered question suggests that Pesach Hallel is restricted because of the fallen Egyptians (according to the Shibolet Haleket, whoever that is). But, as noted in that question, we don't do that for the festival (chag) days in Pesach, which seems unusual if that's the reason. Also, if this is the reason, is there a different reason for reducing the Rosh Chodesh Hallel?¹

  
  


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  Perhaps chol ha-moed "should" have the reduced Hallel for both, but Sukkot is zman simchateinu (the time of our rejoicing) so we increase our joy by increasing Hallel. I've never heard anybody make that argument; I'm just guessing here.

  
  

Can anybody provide a sourced explanation for why Hallel varies between the two chol ha-moed periods? If along the way an answer also explains why Rosh Chodesh is treated the way it is that'd be great, though my primary question is about the chagim.

¹ Except in Chanukah, according to the siddur I used this morning. I might ask a separate question about that.

Answer

The Talmud asks this question. The Yerushalmi (Sukkah 5:1) answers simply that Hallel is read all week on Sukkot due to the ongoing Mitzva of the Lulav (which is taken and waved during Hallel). The Bavli (Arachin 10) answers that since each day of Sukkot has its own unique Korban Musaf (the number of bulls changes each day, cf. Numbers 29) then in a certain way each day is its own holiday with its own Hallel, unlike Pesach which has the same Korban Musaf every day (Numbers 28:24) for which one Hallel suffices. See here where R Chaim Soloveitchik is cited as ruling that one needs one Hallel for all the days of Pesach, and if one missed saying it on the first day, he says it on any subsequent day. (Note that adding "half Hallel" on any day is a later custom as a way to mark days which are special but don't have a formal Hallel obligation.)

See too this article on the subject.